{
 "cells": [
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 感知机(Perceptron)\n",
    "## 1.1 基本概念\n",
    "感知机是最早的神经网络模型之一，由 Frank Rosenblatt 在 1957 年提出。它是一种二元线性分类器，用于处理二分类问题。感知机模型的基本思想是寻找一个超平面，能够将两类样本完全正确地划分开。\n",
    "## 1.2 关键技术\n",
    "感知机的关键技术包括权重和偏置。权重是用来控制输入特征对输出结果的影响程度，偏置是用来控制当所有输入特征都为零时的输出值。<br/>\n",
    "![image.png](../images/1-perceptron-network.webp)<br/>\n",
    "感知机的工作原理可以用以下数学公式表示：<br/>\n",
    "![image-2.png](../images/1-perceptron-math.webp)<br/>\n",
    "其中， 是权重， 是输入特征， 是偏置。<br/>\n",
    "## 1.3 应用领域\n",
    "感知机主要用于处理二分类问题，如垃圾邮件检测、图像识别等。\n",
    "\n",
    "## 1.4 优点\n",
    "感知机模型简单易懂，计算效率高，适合处理线性可分的二分类问题。\n",
    "\n",
    "## 1.5 缺点\n",
    "感知机模型的主要缺点是只能处理线性可分的问题，对于非线性可分的问题，感知机无法找到一个有效的超平面来正确分类。\n",
    "\n",
    "## 1.6 实例分析\n",
    "感知机是许多更复杂的神经网络模型的基础，如多层感知机 (MLP)。在 MLP 中，感知机被用作基本的计算单元，通过堆叠多层感知机，MLP 能够处理更复杂的问题。\n",
    "\n",
    "## 1.7 手动实现\n",
    "感知机的手动实现主要包括权重和偏置的初始化，以及权重和偏置的更新。在每次迭代中，感知机会根据预测结果和真实结果的差异来更新权重和偏置，直到找到一个能够正确分类所有样本的超平面。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 以下是一个简单的感知机的 Python 实现，并对比可视化原始数据和预测数据：\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "class Perceptron:\n",
    "    def __init__(self, learning_rate=0.01, n_iters=1000):\n",
    "        self.lr = learning_rate\n",
    "        self.n_iters = n_iters\n",
    "        self.activation_func = self._unit_step_func\n",
    "        self.weights = None\n",
    "        self.bias = None\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        n_samples, n_features = X.shape\n",
    "\n",
    "        # 初始化权重和偏置\n",
    "        self.weights = np.zeros(n_features)\n",
    "        self.bias = 0\n",
    "\n",
    "        y_ = np.array([1 if i > 0 else 0 for i in y])\n",
    "\n",
    "        for _ in range(self.n_iters):\n",
    "            for idx, x_i in enumerate(X):\n",
    "                linear_output = np.dot(x_i, self.weights) + self.bias\n",
    "                y_predicted = self.activation_func(linear_output)\n",
    "\n",
    "                # 更新权重和偏置\n",
    "                update = self.lr * (y_[idx] - y_predicted)\n",
    "                self.weights += update * x_i\n",
    "                self.bias += update\n",
    "\n",
    "    def predict(self, X):\n",
    "        linear_output = np.dot(X, self.weights) + self.bias\n",
    "        y_predicted = self.activation_func(linear_output)\n",
    "        return y_predicted\n",
    "\n",
    "    def _unit_step_func(self, x):\n",
    "        return np.where(x>=0, 1, 0)\n",
    "\n",
    "# 测试感知机\n",
    "def main():\n",
    "    # 创建数据\n",
    "    np.random.seed(42)\n",
    "    X = np.random.rand(100, 2)\n",
    "    y = np.where(X[:, 0] > X[:, 1], 1, 0)\n",
    "\n",
    "    # 训练感知机\n",
    "    p = Perceptron(learning_rate=0.1, n_iters=100)\n",
    "    p.fit(X, y)\n",
    "\n",
    "    # 预测\n",
    "    y_pred = p.predict(X)\n",
    "\n",
    "    # 可视化结果\n",
    "    fig, ax = plt.subplots(1, 2, figsize=(10, 5))\n",
    "    ax[0].scatter(X[:, 0], X[:, 1], c=y)\n",
    "    ax[0].set_title('Original Data')\n",
    "    ax[1].scatter(X[:, 0], X[:, 1], c=y_pred)\n",
    "    ax[1].set_title('Predicted Data')\n",
    "    plt.show()\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    main()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "notes",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
